Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Find (a) $f_{x}(x, y),$ (b) $f_{y}(x, y)$ at the indicated point.$$f(x, y)=3 x^{2} y^{3} e^{-4 x^{3} y^{2}}(2,-1)$$

$564 e^{-32}$(b) $-732 e^{-32}$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 2

Partial Derivatives

Missouri State University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

03:10

Find (a) $f_{x}(x, y),$ (b…

02:23

02:34

02:37

Given $f(x, y)=y^{3}-3 y x…

00:44

Find $f_{x}$ and $f_{y}$

00:37

Find $f_{x}$ and $f_{y}$ w…

02:16

Find(a) $f^{\prime \pr…

00:38

So this is, in some sense a continuation of ah, problem 10 because we actually already found the partial derivative of that function in number 10. So if you haven't done number 10 or haven't watched the video of number 10, I would go and watch that one first. Because we actually go through how we get these two partial derivatives there. Um, so just to save some time, if you've already seen that one at this point, it's just going to be us plugging in these values into each of these equations. Um, so remember, this is saying like X is equal to y is equal to negative one. So when I come over here and do f partial of to negative one, I'm just gonna plug in to for X negative one for why eso that should give So six times two and then negative one cute would just be negative one and then e to the negative or times two cubes. About eight y squared is one. And then times one minus six X cube. So again, that's eight. And then why square one? Uh, that would go ahead and multiply all this together, so that would be what? Negative 12 and then e to the negative. 32. And then over here, that would be negative. 47 It looks like, um and then we can go ahead and multiply those together, which should give us 564. Um, so 564 eat the negative. 32 and then over here. And so maybe I should write f so that's to negative one. And we'll do the same thing over here, so just broke into negative one. So that will give three. And then it would be four times one and then e to the bowl. This is the same Power is over there, so that should just be negative. 32. And over here, three times three minus eight, uh, times eight times one. And so that would give us 12 e to the negative. 32 then 64 minus three. So that would be negative. 61. And we multiply those to the together. We should get negative. 732 e to the negative. 32. And so that is our personal. The perspective. Why at the point, Negative too. Alright. So again, remember, if you haven't watched the video on number 10 on how we ended up getting thes two partials here, go back and watch that, Um because otherwise it might be kind of hard to make the logical conclusion of how to get these if you didn't do those previous steps.

View More Answers From This Book

Find Another Textbook

06:48

Find the partial derivatives with respect to (a) $x$ and (b) $y$.$$f(x, …

01:23

Find and classify, using the second partial derivative test, the critical po…

01:58

Evaluate the given integral and check your answer.$$\int \sqrt{t} d t$$<…

04:06

Sketch some of the level curves (contours) or the surface defined by $f$.

01:52

Evaluate the given integral.$$\int\left(3 e^{x}-2 e^{y}+2 x-3 y+5\right)…

01:53

Evaluate the given integral and check your answer.$$\int\left(\frac{5}{x…

03:01

Determine the area of the region bounded by the given curves.The region …

03:34

Use the method of Lagrange multipliers to optimize $f$ as indicated, subject…

09:45

Find the partial derivatives with respect to (a) $x,$ (b) $y$ and (c) $z$.

01:48